脆性材料破坏模拟的网格生成算法

A mesh generation algorithm for simulation on fracture and fragmentation of brittle materials

脆性材料的破坏过程具有随机性,当前的网格生成算法没有充分考虑脆性材料破坏时裂纹扩展和碎块生成的随机性。在Persson网格生成算法与Delaunay随机网格剖分理论基础上,提出了一种可根据模拟需要动态控制网格品质的网格生成算法。通过对随机分布点的Delauna三角化,生成初始网格,然后将网格体系比拟为桁架结构,网格节点即为桁架节点。桁架节点在虚拟力作用下可动态调整位置,并最终达到整个体系受力平衡。对Persson算法中的尺寸分布函数和收敛条件进行了修正,从而提高了收敛速度,并适用于任意形状对象的网格剖分。基于VC++平台开发了算法程序。通过实例对算法进行了验证,表明算法能够满足脆性材料破碎模拟的需要。

The fracture of brittle materials is a typically random process.The randomness has not been fully reflected in the existing mesh generation method,especially for the randomness of crack extension and fragments formation.In this study,an algorithm,which can dynamically control mesh quality,has been introduced on the basis of Persson＇s algorithm and Delaunay triangulation theory.The initial grid has been first generated by the Delaunay triangulation of random distribution points.Then the initial mesh can be improved by solving for equilibrium in a truss structure.Mesh points are nodes of the truss.The locations of truss nodes can be dynamically adjusted by the fictitious forces up to achieving a stable state.The convergence rate is significantly improved by modifying the mesh size function and convergence condition of Persson＇s method.Moreover,the algorithm can be suitable to arbitrary complex shaped object.The algorithm has been completed in C＋＋ language.Several examples are given to illustrate the validity of this algorithm,which indicates that the algorithm can meet the requirements of simulation on the fracture and fragmentation of brittle materials.